The forced turn-back of asylum seeker boats to Indonesia has overwhelming public support in Australia, bolstering Prime Minister Tony Abbott as he sits down on Wednesday with President Susilo Bambang Yudhoyono.

A new poll also finds almost two-thirds of Australians back spying operations in Indonesia, another flashpoint for Mr Abbott to navigate after last year's revelations that Australia bugged Mr Yudhoyono's telephone.

Yet in a surprise result, the public is just about as happy to treat America - or even New Zealand - as an intelligence target a finding apparently at odds with Australians' strong support for the ANZUS alliance.

An orange lifeboat used to send asylum seekers back to Indonesia. Photo: Supplied

But it is ties with Indonesia where Australians appear most concerned, with controversy over classified documents leaked by Edward Snowden and Indonesian anger at boat turn-backs the dominant themes of recent months.

About 40 per cent believe relations with Indonesia are worsening, compared with 16 per cent in the same survey last year.

While this is still below a low point of 47 per cent in 2006, soon after the sentencing of Schapelle Corby, far fewer people now see a prospect for improvement in the relationship.

President Yudhoyono finds little favour among Australians, with 28 per cent reporting no admiration for the Indonesian leader.

This is despite Mr Abbott's assurance, repeated again on Tuesday, ''he has been a great friend to Australia''.

Mr Abbott deflected questions about friction in the Indonesia relationship over the boat turn-backs by pointing to the sharp drop in attempted voyages over recent months.

''Because none of them are making it to Australia, very few of them are leaving Indonesian shores. The whole point of leaving Indonesia is to get to Australia and if you never get to Australia, why bother leaving Indonesia?'' Mr Abbott told ABC radio.

The Prime Minister's turn-back policy is backed by 71 per cent of Australians.

The Lowy poll ranks a list of ''threats to Australia's vital interests'', with international terrorism (65 per cent) and nuclear weapons in the hands of unfriendly countries (64 per cent) sparking most concern.

The nationwide survey of 1000 taken in February also shows strong support for offshore processing of asylum seekers, but in a sign of community divisions over boat arrivals, 57 per cent disagreed that ''no asylum seeker coming to Australia by boat should be allowed to settle in Australia''.